The title basically says it all. Is it possible to associate with each pair of reals, another unique real? I guess you could say I'm looking for functions of two real arguments that return a distinct real number.
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Recall that the reals are in bijection with $2^{\Bbb N}$ via dyadic fractions. – Adam Hughes Feb 03 '15 at 19:13
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The accepted answer to Examples of bijective map from $\mathbb{R}^3\rightarrow \mathbb{R}$ covers several ways to do so and does it very thoroughly. – Brian M. Scott Feb 03 '15 at 19:40